The Archimax copula, which generalizes the Archimedean and the bivariate extreme value copulas, is considered. It is shown that the stochastic increasing property of an Archimax copula is inherited from its associated Archimedean copula. The calculation of Kendall?s tau and Spearman?s rho for Archimax copulas is reviewed. A new explicit integral representation for Spearman?s rho of the Gumbel-Hougaard Archimax copula is obtained. Based on a checkerboard approximation of copulas in the topology of uniform convergence, we use the obtained results to provide a numerical evidence for the validity of an open conjecture by Hutchinson-Lai, which states bounds on Spearman?s rho in terms of Kendall?s tau under the stochastic increasing dependence property.